The Name Worshippers of Mount Athos had been shut down. What mattered most were the defiant interruptions to the angry sermon of Archbishop Nikon of Vologda, who had marched into the monastery courtyard behind the troops. “You mistakenly believe that names are the same as God,” his voice trembled. “But I tell you that names, even of divine beings, are not God themselves.” Corralled, water-drenched, their arms twisted violently behind their backs, the monks would not be silenced. “Imia Bozhie est’ sam Bog!” some of them were clearly heard shouting, their eyes alight. “The Name of God is God!”

…Throwing himself into set theory back in Moscow, Luzin maintained strong ties with Florensky, and here is where the escapades of the monks of the Aegean return to our story. It is not clear precisely when both men first learned of Name Worshipping, but already in 1906 they enjoyed calling each other by names other than their own. When news of the rebellion on Mount Athos reached Russia in 1913, Florensky spoke up publicly in its favor, and befriended monks who had endured firsthand the navy’s brutal attack on St. Pantaleimon. Soon two worlds were becoming entwined. Lebesgue had asked whether a mathematical object could exist without defining (meaning naming) it, and now the answer was becoming clear. Just as naming God via glossolalian repetition was a religious act that brought the deity into existence, so naming sets via increasingly recursive definitions was a mathematical act that conferred a reality in the world of numbers. Cantor and before him the ancient Neoplatonists had shown the way, but this was only the beginning. Infused with mysticism, Florensky believed, new forms of mathematics and religion were being born, ones that by rejecting determinism would rescue mankind from catastrophe. In both cases—God and infinity—the key to bringing abstractions into reality was bestowing upon them a name.

A copy of Naming Infinity is winging it’s way to me, and I’d like to invite commenters here to read along at home and contribute posts and comments in February. I’m hoping this can be like last summer’s Sondheim Symposium, where some of you watched Company and Passion with me, and contributed posts with enough context to let everyone follow along.

I’m going to try and hassle some of my offline friends into doing this, and if you’re interested in reading and posting along, please email me (leahDOTlibrescoATgmailDOTcom) and sound off in the comments.

To introduce a talk on “Big Numbers,” I invite two audience volunteers to try exactly this. I tell them the rules:

You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.

…Place value, exponentials, stacked exponentials: each can express boundlessly big numbers, and in this sense they’re all equivalent. But the notational systems differ dramatically in the numbers they can express concisely. That’s what the fifteen-second time limit illustrates. It takes the same amount of time to write 9999, 9999, and yet the first number is quotidian, the second astronomical, and the third hyper-mega astronomical. The key to the biggest number contest is not swift penmanship, but rather a potent paradigm for concisely capturing the gargantuan.

Such paradigms are historical rarities. We find a flurry in antiquity, another flurry in the twentieth century, and nothing much in between. But when a new way to express big numbers concisely does emerge, it’s often a byproduct of a major scientific revolution: systematized mathematics, formal logic, computer science. Revolutions this momentous, as any Kuhnian could tell you, only happen under the right social conditions. Thus is the story of big numbers a story of human progress.

Leah, your writing is all kinds of awesome. I too am a bookish, Joss Whedon-loving, musical-belting geek who is considering Catholicism after a long trip in the fields of agnosticism. I have nothing to add but to ask you to keep writing.

dave

(I apologize for not knowing how to format this as other than plain text.)

Ages ago, my freshman calculus professor boggled my mind by asking me two questions. First, how many real numbers exist between zero and one? An infinite number. Second, how many exist if you take away all the numbers that have a 3 anywhere in their representation? STILL AN INFINITE NUMBER! Mathematically, the answer was obvious. Yet to my non-infinite mind, it seemed a contradiction. I finally found peace with the idea by realizing that infinity doesn’t have the same restraints as this finite world.

Years later, reading the Catechism of the Catholic Church, I came upon a quote by St. Gregory of Nazianzus:

“I give you but one divinity and power, existing one in three, and containing the three in a distinct way. Divinity without disparity of substance or nature, without superior degree that raises up or inferior degree that casts down. . . the infinite co-naturality of three infinites. Each person considered in himself is entirely God. . . the three considered together. . . I have not even begun to think of unity when the Trinity bathes me in its splendor. I have not even begun to think of the Trinity when unity grasps me. . .” (http://www.scborromeo.org/ccc/p1s2c1p2.htm)

The math helped me to grasp the Trinity as more than just word play, “three in one and one in three”. From childhood I had learned that God is infinite. It is precisely this infinite nature that permits the Trinity, with no violation of math!

http://www.mccaughan.org/g/ g

Dave: you might be amused by the following marginally related fact: the sum of the reciprocals of all the positive integers 1/1+1/2+1/3+1/4+… is infinite, whereas the corresponding sum with the numbers containing 3 omitted 1+1/2+1/4+… is finite. There’s a good sense in which leaving out the numbers containing 3 really does give you a much smaller set, whether you’re talking about the integers or the real numbers between 0 and 1.

http://last-conformer.net/ Gilbert

I’m probably in, but I need to read the book before I know if I have anything worthwhile to say.

leahlibresco

Woo!

TheresaL

What level of commitment are we making if we tell you we’re in? I just put a hold on the book at the library, but I’m not sure I’ll get through it by February.

Are you starting a monthly book club or is this an occasional thing?

Thanks for the Litany.

http://taraseguinwrites.wordpress.com Tara S

I am waiting for someone to write a philosophical/metaphysical treatise in Boolean or similar. I would not understand it, but I would greatly enjoy its existence.

http://thoughtfulatheist.blogspot.com/ Jake

I just ordered my copy from amazon, if only because I was suprely frustrated by last summer’s Sondheim series, which I didn’t get around to watching.

For reasons that remain unclear, Amazon says my copy won’t arrive until the end of January. Curses!

Mitchell Porter

I have access to the book and will presumably have something to say about it.

grok87

I’m in for the book club. Looks like an interesting book… Thanks for the Litany (which I finished) and the Aaronson essay (which I enjoyed but only got halfway through). I liked the Archimedes story. Problem 188 on project euler deals with tetration.

Also thanks for the pointer to Diane Duane’s young wizard’s series. Just ordered the first one on paperbackswap.

leahlibresco

Oh yay!

deiseach

I now fully comprehend the reasoning of the Orthodox Church that the radiance of God can be perceived as light and bliss by the blessed but a tormenting fire by the damned:

“Paradise and hell are the same reality. This is what is depicted in the portrayal of the Second Coming. From Christ, a river of fire flows forth. It is radiant like a golden light at the upper end of it, where the saints are. At its lower end, the same river is fiery, and it is in that part of the river that the demons and the unrepentant (“the never repentant” according to a hymn) are depicted. ”

All you mathematically-gifted will be rejoicing at the prospect of doing problems, so that will be your heaven, and I will be in hell faced with the same prospect

And in the context of mathematics (computing) and theology, for those who may not have read it, Arthur C. Clarke’s The Nine Billion Names of God.

Adrian Ratnapala

Yep, I always thought that story fitted Christianity better than it did Buddhism. Now I know where the idea come from.

Thomas

I’m in if that’s ok.

Fans of David Bentley Hart (I think there are a few who frequent the comments here) might be interested in what he’s written about infinity (http://tinyurl.com/afsjxlm).

leahlibresco

Great, I’ll add you to the list.

paul

i love David Bentley Hart! I think Leah would love his book “The beauty of the infinite”.

jenesaispas

I can’t do it, but had a quick look at the reviews on Amazon and it doesn’t sound all that good, one review says that the people on the front cover are hardly mentioned in the book which seems odd.

I will second (third?) the recommendation of David Bentley Hart. His prose is neither easy nor light, but it is scathing in its wit, luminous in its insights, and utter bliss to any lover of the English language. Dense and difficult, but infinitely rewarding.